The Collatz Conjecture and Cryptography: A Tale of Computational Complexity
2025-03-15
This article explores the infamous Collatz conjecture and its surprising connection to ARX algorithms in cryptography (e.g., ChaCha). The Collatz conjecture describes a simple iterative function; whether it always converges to 1 remains unproven. The article draws an analogy between the Collatz function and a Turing machine, highlighting how carry propagation in its bitwise implementation creates unpredictable complexity. This contrasts interestingly with ARX algorithms, which use addition, rotation, and XOR to achieve efficient diffusion. The article suggests the Collatz conjecture's unsolved nature might stem from the inherent complexity of computation, similar to the halting problem.